NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 2

In the questions, below find the types of decimals.

Q.III) 64455

pq Is terminating if

  • p and q are co-prime

  • q is of the form 2n5m Where n and m are non-negative integers

Checking Co-prime

64 and 455 have no common factors, so, 64 and 455 are co-prime

For denominator 455

Given the factors and find the factor of 455

Given the Factors of 455

Given the factors and find the factor of 455

Hence 455=5×7×13

Denominator=5×7×13

So, denominator is not of the form 2n5m

Thus 64455 has a non-terminating repeating decimal

Q.IV) 151600

151600=3320

pq Is terminating if

  • p and q are co-prime

  • And q is of the form 2n5m Where n and m are non-negative integers

Checking Co-prime

3 and 320 have no common factors, so, 3 and 320 are co-prime

For denominator 320

Image describing the factorization of 320

Factorization of 320

Image describing the factorization of 320

Hence 320=2×2×2×2×2×2×5

=26×51

Denominator=26×51

So, denominator is of the form 2n5m

Where n=6,m=1

Thus 3320 i.e. 151600 is terminating decimal

Q.V) 29343

pq Is terminating if

  • p and q are co-prime

  • And q is of the form 2n5m Where n and m are non-negative integers

Checking Co-prime

29 and 343 have no common factors, so, 29 and 343 are co-prime

For denominator 343

Image describing the factorization of 343

Factorization of 343

Image describing the factorization of 343

Hence 343=7×7×7

=73

Denominator=7×7×7

So, denominator is not of the form 2n5m

Thus 29343 has a non-terminating repeating decimal

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